This clinical trial is being developed to treat patients with advanced Merkel cell carcinoma (stage 3b or 4) off-label with the FDA-approved drug ipilimumab at the NIH Clinical Research Center and at Memorial Sloan-Kettering Cancer Center in New York. The manufacturer is supplying the drug, and a final agreement regarding the clinical trial is being negotiated with them. Concurrently the trial protocol is being developed and will soon undergo internal scientific review. Patients will be treated with ipilimumab and followed to monitor clinical response. In addition, tumor specimens and blood will be collected to evaluate anti-tumor immune responses during treatment.